There is no history, since any letter can be used. The letters can be from the Greek or Roman or other alphabets, they can be upper case or lower case.
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The letters b and c could represent almost any number. They are used in equations normally because they are unknown, and so that we can figure out their values through solving the problem.
variable expression, I believe.
A letter or symbol used to represent an unknown quantity is typically called a variable. In mathematics, common variables include letters such as ( x ), ( y ), and ( z ). These variables can stand for different values in equations and expressions, allowing for the representation of general cases and relationships between quantities.
In programming: They let you do generic calculations, with numbers that you don't know in advance. In algebra: They let you do calculations with unknown values - either generic calculations, or do calculations to find such unknown values in a specific case.
The mathematician David Hilbert used names of colors, such as "white" and "black," to represent unknown values in his work in mathematics and logic. This approach was part of his concept of "Game Semantics" where colors were used to represent players and moves in mathematical games, allowing for the study of logical systems.